For reference, the quote was:
> We believe you will agree that it is undesirable for our companies to make simultaneous use of "the real thing" in connection with our respective products.
I read that like Coke thought the publisher didn't necessarily realize there was a dual usage of the slogan, and that once they did they would immediately agree with the only obvious conclusion which is that it's bad for business. And if the publisher did previously realize, this is simply pointing out that they were acting in bad faith with respect to Coke and stupidly with respect to themselves.
And of course the publisher's reply was that they weren't competing in the same market and therefore there was no confusion over the slogan. Not sure if it was a trademark, but that's how trademark law works today. In fact Coke is required to defend its trademarks.
In summary, someone who does something you don't like doesn't necessarily do so because they consciously disagree with your position. Hanlon's razor, more or less.
I agree that depending on the circumstances, meta-language about the argument being had is a kind of bullying - "Let's be reasonable about this." - but it also hints as to the weakness of the bully's position.